Acta Scientific Computer Sciences

Research Article Volume 4 Issue 6

Extreme Value Charts and ANOM Based on Gumbel Distribution

B Srinivas Rao1, C Chinnamamba2*, K Rosaiah3 and J Pratapa Reddy4

1R.V.R and J.C College of Engineering, Chowdavaram, Guntur, Andhra Pradesh, India
2KL University, Vaddeswaram, Vijayawada, Andhra Pradesh, India
3Department of Statistics, Acharya Nagarjuna University, Guntur, India
4St.Ann's College for Women Gorantla, Guntur, Andhra Pradesh, India

*Corresponding Author: C Chinnamamba, KL University, Vaddeswaram, Vijayawada, Andhra Pradesh, India.

Received: March 21, 2022; Published: May 30, 2022

Abstract

The quality is assessable by its feature is implicit with a probability model which follow Gumbel distribution. From each subgroups extreme values are used to construct extreme value charts and variable control charts. Probability model of the extreme order statistics and the size of each sub group are used in control chart constants. To find the decision lines of Gumbel distribution we implement a method of analysis of means (ANOM). The proposed ANOM decision lines are constructed for given number of subgroup within means category and between means category given by Ott (1967). These decision lines are illustrated by giving few examples.


Keywords: Analysis of Means; Statistical Control; Quantile - Quantile Plot; Control Limits

References

  1. Bakir ST. “Analysis of means using ranks for randomized complete block designs”. Communications in Statistics- Simulation and Computation 23 (1994): 547-568.
  2. Bernard AJ and Wludyka PS. “Robust i-sample analysis of means type randomization tests for variances”. Journal of Statistical Computation and Simulation 69 (2001): 57-88.
  3. Dedewicz EJ and Nelson PR. “Heteroscedastic analysis of means (hanom)”. American Journal of Mathematical and Management Sciences 23 (2003): 143-181.
  4. Enrick NL. “An analysis of means in a three-way factorial”. Journal of Quality Technology 8 (1976): 189-196.
  5. Farnum NR. “Analysis of means tables using mathematical processors”. Quality Engineering 16 (2004): 399-405.
  6. Guirguis GH and Tobias RD. “On the computation of the distribution for the analysis of means”. Communication in Statistics- Simulation and Computation 16 (2004): 61-887.
  7. Gunst RF., et al. “Statistical design and analysis of experiments”. John Wiley and Sons, New York (1989).
  8. Montgomery DC. “Design and analysis of experiments”. fifth ed., John Wiley and Sons (2000).
  9. Nelson PR., et al. “Power curves for analysis of means for variances”. Journal of Quality Technology 33 (2001): 60-65.
  10. Nelson PR and Dudewicz EJ. “Exact analysis of means with unequal variances”. Technometrics 44 (2002: 115-119.
  11. Ohta H. “A procedure for pooling data by analysis of means”. Journal of Quality Technology 13 (1981): 115-119.
  12. Ott ER. “Analysis of means- a graphical procedure”. Industrial Quality Control 24 (1967).
  13. Ramig PF. “Application of analysis of means”. Journal of Quality Technology 15 (1983): 19-25.
  14. Rao CV and Prankumar M. “Anom-type graphical methods for testing the equality of several correlation coefficients”. Gujarat Statistical Review 29 (2002): 47-56.
  15. Rao CV. “Analysis of means- a review”. Journal of Quality Technology (2005): 37.
  16. Schilling EG. “A simplified graphical grant lot acceptance sampling procedure”. Journal of Quality Technology 11 (1979): 116-127.
  17. Srinivasa Rao B., et al. “Extreme Value Charts and ANOM Based on Inverse Rayleigh Distribution”. Pakistan Journal of Statistics and Operations Research4 (2012): 759-766.
  18. Srinivasa Rao B., et al. “Extreme Value Charts and Analysis of Means (ANOM) Based on the Log Logistic Distribution". Journal of Modern Applied Statistical Methods2 (2012): 493-505.
  19. B Srinivasa Rao and P Sricharani. “Extreme value charts and Analysis of means based on Dagum distribution”. International Journal of Statistics and Applied Mathematics2 (2018): 351-364.
  20. R Subba Rao., et al. “Analysis of Means (ANOM) based on the Size Biased Lomax Distribution”. International Journal of Engineering and Technology3.31 (2018): 129-132.
  21. Kalanka P Jayalatha Hon Keung Tony Ng. “Analysis of means approach in advanced designs”. (2020).
  22. Kalanka P Jayalath and Jacob Turner. “Analysis of Means (ANOM) Concepts and Computations”. Applications and Applied Mathematics: An International Journal1 (2021): 75-96.
  23. B Srinivasa Rao and KNVR Lakshmi. “Analysis of Means (ANOM) based on New-weibull Pareto distribution”. International Journal of Research and Analytical Reviews2 (2021): 481-491.
  24. Anil A and B Srinivasa Rao. “Extreme Value Charts and Analysis of Means based on New Weighted Exponential distribution”. Journal of University of Shanghai for Science and Technology11 (2021): 825-836.

Citation

Citation: C Chinnamamba., et al. “Extreme Value Charts and ANOM Based on Gumbel Distribution". Acta Scientific Computer Sciences 4.6 (2022): 30-36.

Copyright

Copyright: © 2022 C Chinnamamba., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.




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